Method for temperature-compensated accelerometer measurement, with at least a device comprising two vibrating resonators

ABSTRACT

The invention concerns a temperature-compensated accelerator measurement using two vibrating resonators whereof the frequencies (f 1 , f 2 ) are measured, then used for determining ( 18, 19 ) the most probable temperature value (T) based on the sum f 1 +f 2  and on a pre-established correlation ( 14 ) between the temperature and the sum f 1 +f 2  and finally based on the determination ( 20 ) of the amount f 1 −f 2  of the weighted temperature value, calculating ( 21 ) the temperature compensated value of the acceleration (γ).

FIELD OF THE INVENTION

The present invention relates to the field of accelerometricmeasurements, and more specifically it relates to improvements made inthe field of accelerometric measurements performed with devices havingtwo vibrating resonators working respectively in stress states ofopposite signs (in general in tension and compression).

DESCRIPTION OF THE PRIOR ART

Thus, the use is already known of devices having two vibratingresonators comprising two respective vibrating beams, parallel andidentical, one working in tension and the other in compression, todetect a component of acceleration (see for example documents FR 0010675 and FR-A-2 784 752 in the name of the Applicant; FR-A-2 685 964,FR-A-2 784 752). As illustrated by way of example in FIG. 1 of theappended drawings, such an accelerometer device 1 comprises, in a veryschematic manner, the two miniature accelerometers Acc₁, Acc₂ withnonslaved pendular masses. Each of them comprises a pendulum mass (orseismic mass) M urged toward a rest position by a link with a stand Swhich consists of a vibrating beam or blade P (the means of vibrationalexcitation and of detection of the vibration not being illustrated) andof a hinge-forming member C. The two beams P₁, P₂ are identical andparallel and are disposed in a reverse position with respect to eachother, so that, under the action of the two respective identical seismicmasses M₁, M₂, one P₁ of the beams works in compression and the other P₂of the beams works in tension. The two individual accelerometers Acc₁,Acc₂ are together enclosed in a leaktight box B in which an intensevacuum is generally established.

When the accelerometer device 1 is subjected to an acceleration γdirected along the sensitive axis, that is to say for exampleperpendicular to the span of the vibrating beams P₁, P₂, it results in avariation of the resonant frequencies of the beams related to theacceleration applied and to the stress (compression or tension)undergone by the beams:f ₁ =f ₀₁ +k ₁₁ γ−k ₁₂γ² +k ₁₃γ³f ₂ =f ₀₂ −k ₂₁ γ−k ₂₂γ² +k ₂₃γ³where f₀₁ and f₀₂ are the resonant frequencies of the two respectivebeams P₁ and P₂ in the absence of acceleration, and the coefficients kare constants.

This type of accelerometer device has several benefits, in particular byreason of its low bulk (flat structure whose thickness may be less than1 mm for in-plane dimensions of the order of a centimeter) and of itssimple and economical fabrication by methods of chemical etching on acrystal wafer, generally piezoelectric, but possibly silicon, withpossibility of simultaneous collective fabrication of severalaccelerometers on one and the same wafer of material.

However, in the type of accelerometer device considered having doublevibrating resonator, the resonant frequencies of the vibrating beams P₁,P₂ depend not only on the acceleration γ to which the device issubjected, but also on the temperature T of the beams. One is thereforeled to supplement the above equations with a polynomial in T:$f_{1} = {f_{01} + {\prod\limits_{1}^{1}\left( \gamma^{n} \right)} + {\prod\limits_{1}^{2}\left( T^{n} \right)}}$$f_{2} = {f_{02} + {\prod\limits_{2}^{1}\left( \gamma^{n\quad} \right)} + {\prod\limits_{2}^{2}\left( T^{n} \right)}}$

A simple calculation of the value of the acceleration γ as a function ofthe measured frequency f₁ and/or f₂ requires knowledge of thetemperature of the beams P₁, P₂. However, it is not possible, inpractice, to dispose an appropriate sensor, in the box B, in immediateproximity to the vibrating beams, nor to dispose a thermal sensor inactual contact with the vibrating beams P₁, P₂ (which would constitutethe ideal solution for obtaining an exact value of the temperature) byreason of the perturbation that the presence of this sensor would causeon the vibration of the beams. Finally, recourse to a method ofthermoelectric measurement would be liable to perturb the temperature ofthe beam itself.

An object of the invention is therefore to propose a method ofcalculating the value of the acceleration, temperature-compensated, onthe basis of the measurements of the frequencies f₁, f₂ of the twovibrating beams P₁, P₂, without the need for recourse to any thermaldetection means disposed in contact with the vibrating beams.

SUMMARY OF THE INVENTION

For these purposes, the invention proposes a method for accelerometermeasurement by determination of the value, compensated as a function oftemperature, of an acceleration on the basis of measurements offrequencies made on one accelerometer device having two vibratingresonators of similar geometries working respectively in stress statesof opposite signs, which process is characterized in that according tothe invention it comprises the steps which follow:

-   -   the device being subjected to a component of acceleration, the        frequencies f₁ and f₂ of the respective vibrations of the two        vibrating resonators are determined, given that the respective        values of these two frequencies are influenced by the        acceleration and by the temperature;    -   the sum f₁+f₂ of the two measured frequencies is determined,        given that this sum is influenced by the temperature;    -   on the basis of a pre-established correlation of the variation        of the quantity f₁+f₂ as a function of temperature, the possible        temperature values T_(i) corresponding to the value of the        abovedetermined sum f₁+f₂ are plotted;    -   the value (G_(mes)) of a magnitude representative of the        temperature in proximity to the device having two vibrating        resonators is measured;    -   with the aid of a previously established transfer function H, an        estimated value G_(estimated)=H(G_(mes)) of abovesaid magnitude        is determined on the basis of said measured value G_(mes), this        estimated magnitude being representative of the estimated        temperature of the vibrating resonators;    -   on the basis of the estimated value G_(estimated) of said        magnitude and of the possible temperature values T_(i), the        probability P(T_(i)) that the value of the temperature of the        resonators is T_(i), is determined, for each value T_(i);    -   a weighted value T of the temperature of the vibrating        resonators is calculated T=ΣP(T_(i))×T_(i);    -   finally on the basis of one and/or the measured frequencies f₁        and f₂ and of the weighted value T of the temperature, the        temperature-compensated value of the acceleration undergone by        the accelerometer device is determined.

By virtue of the provisions of the invention, it is possible to takeaccount, in the calculation of the value of the acceleration γ, of atemperature value T, or of a magnitude representative of thistemperature (for example a magnitude varying linearly as a function oftemperature) in the vicinity of the resonators—and hence intrinsicallyinexact since it is not the value of the temperature of theresonators—and on the basis of a choice, involving a probabilitycalculation, between several possible values of the temperature.

In practice, the two vibrating resonators cannot be strictly identicalfrom the geometrical point of view: it is then desirable to take accountof this geometrical difference by correcting the sum f₁+f₂ with an errorterm estimated on the basis of the acceleration calculated during theprevious calculation cycle, if it exists.

Again in practice, the implementation of the method of the inventionwith a polynomial π(T^(n)) of the high order n turns out to be complex,by reason of the high number n of mathematical solutions, that is to sayof the number n of possible values of temperature T_(i) corresponding toa given value of the frequency f₁+f₂. This also results in a longercalculation of the probabilities P(T_(i)) and of the valueT=ΣP(T_(i))×T_(i). A value T of sufficient accuracy is obtained, in aconcrete manner, with a polynomial of order 2: π(T²) or of order 3:π(T³).

The mathematical relation between the frequency, the acceleration andthe temperature may be writtenf=f ₀+π(γ³)+a(T−T _(o))²in the case of a polynomial in T of order 2 andf=f ₀+π(γ³)+a(T−T _(o))² +b(T−T _(o))³in the case of a polynomial in T of order 3.

In practice, the terms in γ² and γ³ are small and may be neglectedcompared with the term in γ. The two equations above may then be writtenin respectively simplified form:f=f ₀ +kγ+a(T−T _(o))²and f=f ₀ +kγ+a(T−T _(o))² +b(T−T _(o))³

The curve corresponding to the function f(T) is a parabola or a cubic,respectively, whose local extremum (situated in the bracket of theimplementation temperatures) corresponds to the reversal temperature (or“turnover”) temperature T_(o). Thus, with each value f of the frequencymay be associated two possible values of temperature T_(a) and T_(b),just one of which is the exact temperature of the vibrating resonator.In the case of a third-order polynomial, the third solution is spuriouswith respect to the temperature domain considered and may be rejectedoutright. The determination of the temperature of the resonators callsupon a probabilistic estimation and consists in associating, with thesum f₁+f₂, two values T_(a) and T_(b), in calculating the probabilityP(T_(a)) that the temperature of the resonators is T_(a) and theprobability P(T_(b)) that the temperature of the resonators is T_(b),then in calculating a weighted value of the temperature of theresonatorsT=P(T _(a))×T _(a) +P(T _(b))×T _(b).

In the case of accelerometric and/or gyroscopic measurements in severalaxes (in practice in two or three axes of a reference system) with theaid of several respective accelerometric and/or gyroscopic and/orgyrometric vibrating devices (inertial sensor block), provision mayadvantageously be made for a value of the temperature-compensatedacceleration to be determined, in each axis, according to one or otherof the processes set forth above and, in respect of the determination ofone at least of the values of the temperature-compensated acceleration,for the weighted value of temperature determined for the vibratingdevice associated with this axis together with at least one weightedvalue of temperature determined for at least one vibrating deviceassociated with at least one other axis to be used as weightedtemperature value.

Such an implementation is most particularly beneficial in the case whereall the vibrating resonators of the accelerometric and/or gyroscopicand/or gyrometric devices are machined from one and the same block ofcrystal.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood on reading the detaileddescription which follows of certain embodiments given by way ofnonlimiting examples. In this description, reference is made to theappended drawings in which:

FIG. 1 is a very schematic representation of a prior art accelerometerdevice having two vibrating resonators;

FIG. 2 is a very schematic representation of an accelerometer devicehaving two vibrating resonators and arranged in accordance with theinvention;

FIGS. 3A and 3B are block diagrams respectively illustrating twopreferred implementations of the method in accordance with theinvention;

FIG. 4 is a block diagram illustrating an improvement of the method ofFIG. 3A;

FIG. 5 is a block diagram illustrating in a simplified manner anexemplary inertial sensor arrangement implementing the provisions of theinvention;

FIG. 6 is a block diagram, mimicking that of FIG. 3A, detailing afunctional part of the inertial sensor of FIG. 5;

FIG. 7 is a block diagram illustrating a variant embodiment of a portionof the functional part of FIG. 6; and

FIG. 8 is a block diagram, mimicking that of FIG. 3A, illustrating yetanother variant embodiment.

DETAILED DESCRIPTION OF THE INVENTION

The invention is aimed at determining a value, corrected as a functionof temperature, of the acceleration γ undergone by an accelerometerdevice having two vibrating resonators of similar geometries, workingrespectively in stress states of opposite signs. In the exampleillustrated, the two resonators respectively comprise two parallel andsubstantially identical vibrating beams working respectively inparticular in tension and in compression, but possibly being combinablewith at least one other state of stress such as flexion and/or torsion.In the example illustrated, the acceleration γ or the component of theacceleration which is measured is directed substantially perpendicularlyto the beams.

The frequencies of vibration of the two beams may be written, as afunction of temperature T and of acceleration γ:$f_{1} = {f_{01} + {\prod\limits_{1}^{1}\left( \gamma^{n} \right)} + {\prod\limits_{1}^{2}\left( T^{n} \right)}}$$f_{2} = {f_{02} + {\prod\limits_{2}^{1}\left( \gamma^{n\quad} \right)} + {\prod\limits_{2}^{2}\left( T^{n} \right)}}$

According to the invention, the frequencies f₁ and f₂ of the vibrationof the two vibrating beams are determined, and then the sum f₁+f₂ iscalculated.

On the basis of a pre-established and stored correlation between thevalues of frequency and the corresponding values of temperature f→π(Tn),the n possible values Ti of temperature are determined, for thefrequency f1+f2.

An evaluation of the estimated temperature of the resonators is thencarried out. For this purpose, the value G_(mes) of a magnituderepresentative of the temperature in proximity to the device having twovibrating resonators is measured; then, with the aid of a previouslyestablished transfer function H, an estimated value G_(estimated)=H(G_(mes)) of abovesaid magnitude G_(mes) is determined, this estimatedmagnitude being representative of the estimated temperature of thevibrating resonators. On the basis of the estimated value G_(estimated)of said representative magnitude of the estimated temperature of theresonators and of the possible temperature values T_(i), theprobabilities P(T_(i)) that each possible temperature value T_(i) is theexact value of the temperature of the resonators are determined.

A simple way of implementing the above provisions consists in performinga temperature measurement directly, in which case the magnitude Grepresentative of the temperature is the temperature itself. It is inthis context that what follows is set forth.

A temperature sensor that delivers a measured temperature value T_(mes)is disposed in immediate proximity to the box of the accelerometerdevice and either inside, or more readily outside the latter. Byinvoking a transfer function H predetermined through earlier trials, anestimated temperature of the vibrating resonators can be evaluatedT_(estimated)=H(T_(mes)).

The probability P(T_(i)) that the temperature of the resonators is T_(i)is determined on the basis of the values T_(estimated) and T_(i), foreach value T_(i). Then a weighted value T of the temperature isdeterminedT=ΣP(T _(i))·T _(i)that is taken as temperature value of the two resonators.

Thereafter, knowing the temperature T, it is possible to calculate thevalue of the acceleration γ on the basis of one and/or more measuredfrequencies f₁ and f₂.

The implementation of a polynomial π(Tn) of high order n entails complexand lengthy calculations, and makes it difficult to establish thecorrelation f→π(Tn) by reason of the high number of possible values Tiassociated with each frequency value.

Accuracy that is acceptable in practice may be obtained with apolynomial of order 2: π(T²), or preferably of order 3: π(T³).

The vibration frequency is expressed, as a function of acceleration andtemperature, by the relationf=f ₀+π(γ³)+a(T−T _(o))²in the case of a polynomial in T of order 2 or by the relationf=f ₀+π(γ³)+a(T−T _(o))² +b(T−T _(o))³in the case of a polynomial in T of order 3.

The terms in γ² and γ³ being small in practice may be neglected comparedwith the term in γ so that the two aforesaid relations may be written insimplified form, respectively:f=f ₀ +kγ+a(T−T _(o))²and f=f ₀ +kγ+a(T−T _(o))² +b(T−T _(o))³

As represented schematically in FIG. 3, the frequencies f₁ and f₂ of thetwo vibrating resonators P₁ and P₂ subjected to an acceleration γ aremeasured at 10 and 11, given that the frequencies f₁ and f₂ aredependent on γ and on the temperature T, the case of a polynomial oforder 2 in T:f ₁ =f ₀₁ +k ₁ γ+a ₁(T−T _(o1))²f ₂ =f ₀₂ −k ₂ γ+a ₂(T−T _(o2))²(where T_(o1) and T_(o2) are the respective reversal temperatures (or“turnover” temperatures)), or else, in the case of a polynomial of order3 in T:f ₁ =f ₀₁ +k ₁ γ+a ₁(T−T _(o1))² +b ₁(T−T _(o1))³f ₂ =f ₀₂ −k ₂ γ+a ₂(T−T _(o2))² +b ₂(T−T _(o2))³

It is noted that the sum f₁+f₂ is independent of the acceleration γ ifk₁=k₂ and depends only on the temperature. Moreover, the differencef₁−f₂ depends essentially on the acceleration γ if the curvature termsa₁ and a₂, as well as the reversal values T_(o1) and T_(o2) are close toone another, respectively (the terms in T² and T³ dropping out). Themethod in accordance with the invention and which is set forthhereinbelow with regard to FIG. 3A (case of a polynomial of order 2 inT) and FIG. 3B (case of a polynomial of order 3 in T) is based on theexploitation of the two values f₁+f₂ and f₁−f₂.

The sum f₁+f₂ is determined at 12 on the basis of the measurements ofthe frequency f₁ at 10 and of the frequency f₂ at 11.

The two possible values of temperature T_(a), T_(b) corresponding to thevalue f₁+f₂ emanating from the measurements f₁ and f₂ are plotted at 13on the basis of a pre-established correlation, held in memory at 14,between the frequency and the temperature of the resonators (polynomialin T³ and/or T² and T). In the case of a polynomial of order 2 in T(case illustrated in FIG. 3A), the two sought-after values T_(a) andT_(b) are the two solutions of the second-degree equation in T. In thecase of a polynomial of order 3 in T (case illustrated in FIG. 3B), thethird-degree equation in T has three solutions, one of which, however,is spurious with respect to the temperature domain considered and shouldbe rejected; it is thus advisable to hold in memory at 25 (FIG. 3B)limit values, for example T_(min); T_(max), defining the temperaturedomain and to compare at 26 the three solutions of the third-degreeequation with said limit values so as to eliminate the spurious solutionand retain only the two appropriate solutions T_(a), T_(b).

The two temperature values T_(a), T_(b) are the two possible values thatmay correspond to the frequency f₁+f₂, but just one of the twotemperature values is exact in practice.

To perform as accurate an approximation as possible of the exacttemperature of the resonators (the two resonators are assumed to be atthe same temperature), a thermal sensor CTH is disposed in immediateproximity to the resonators. This thermal sensor may be disposed insidethe box B (as shown dashed in FIG. 2), but it may also be disposed(since this is a simpler implementation) outside this box as illustratedin solid line in FIG. 2.

This thermal sensor CTH provides at 15 (FIGS. 3A and 3B) a measuredvalue of temperature T_(mes), which value T_(mes) is only an approximatevalue, and not exact, of the temperature of the resonators P₁, P₂.

Prior to the measurement, a transfer function H is establishedexperimentally between the exact values of temperature of the resonatorsP₁, P₂ situated inside the box B and the temperature values measured,simultaneously, by the sensor CTH outside the box B. The transferfunction H is held in memory at 16.

To fix matters, the transfer function H may be a simple function ofsecond or third order, such as, with H(p)=T(p)/T_(CHT)(P)H(p)=1/(1+αp)²or H(p)=1/[(1+α₁ p)(1+α₂ p)(1+α₃ p)]in which p is the Laplace operator and α, α₁, α₂, α₃ are constantsdepending on the structure of the temperature sensor and on the time forthe heat to propagate between the vibrating beams situated inside thebox B and the temperature sensor CTH situated outside this box.

Thus, with the temperature T_(mes) measured outside the box B, it ispossible to associate at 17, through the transfer function H, anestimated value T_(est) of the temperature of the beams P₁, P₂ insidethe box B.

Then, on the basis of the values T_(a), T_(b) and T_(est), probabilitycalculations are performed at 18 giving the probability P(T_(a)) thatthe temperature T_(a) is the temperature of the beams P₁, P₂ and theprobability P(T_(b)) at the temperature T_(b) is the temperature of thebeams P₁, P₂.

To fix matters, the probabilities P(T_(a)) and P(T_(b)) may becalculated in the following manner:P(T _(a))=g(T _(a))/(g(T _(a))+g(T _(b)))P(T _(b))=g(T _(b))/(g(T _(a))+g(T _(b)))with g(T _(a))=1/(|T _(a) −T _(est)|)g(T _(b))=1/(|T _(b) −T _(est)|)

The calculations could also be performed with the following functions:g(T _(a))=exp(−α·|T _(a) −T _(est)|)g(T _(b))=exp(−α·|T _(b) −T _(est)|)in which α is a constant.

The formulae indicated here have the advantage of being simple and ofleading to fast calculations. However, if necessary, the person skilledin the art may have recourse to formulae that are more complex and moreaccurate, but also entail lengthier calculations.

Then, at 19, is calculated a value T of the temperature which is aweighting of the possible values T_(a) and T_(b) afforded the previouslycalculated weighting coefficients P(T_(a)) and P(T_(b)):T=P(T _(a))·T _(a) +P(T _(b))·T _(b).

A value T of temperature of the resonators which is statistically themost likely is thus defined.

Finally, the temperature-compensated value of the acceleration γundergone by the accelerometer device is determined on the basis of oneof the measured frequencies f₁ or f₂, or on the basis of the twomeasured frequencies f₁ and f₂, and of the weighted value T of thetemperature that has just been determined at 19.

In practice, the quantity f₁−f₂ is calculated at 20. It is known that,in the case of the polynomial of order 2 in T, the mathematicalexpression therefor is:f ₁ −f ₂=(f ₀₁ −f ₀₂)+(k ₁ +k ₂)γ+a ₁(T−T _(o1))² −a ₂(T−T _(o2))

Stated otherwise, this expression is of the type:

 f ₁ −f ₂ =p+qγ+r T+sT ²

On the basis of the value T of the temperature determined at 19, it isthen easy to calculate, at 21, the value γ from T and from f₁−f₂.

In the case of a polynomial of order 3 in T, the mathematical expressionfor f₁−f₂ is more complex, but can nevertheless be determined and alsoallows calculation of the value of γ on the basis of the calculation ofthe value f₁−f₂.

A temperature-compensated value of the acceleration γ is ultimatelyobtained at 22.

The correlation between the frequency and the temperature (T³ and/or T²,T), held in memory at 14, may be stored in the form of a mathematicalequation of second or third degree in T whose coefficients arepre-established by prior experimental measurements performed on theaccelerometer device 1. The two possible values T_(a) and T_(b) are thencalculated by solving this equation for each given value of f₁+f₂. Anarray giving, for all the possible values f₁+f₂, the two correspondingpossible values T_(a), T_(b) may also be held in memory at 14.

In the same way, the transfer function H held in memory at 16 may bestored either in the form of an algebraic relation T_(est)=H(T_(mes)),or in the form of an array of pre-established data giving, for eachvalue T_(mes), the associated value T_(est).

Experience has shown that the curve that mathematically conveys therelation between the frequency and the temperature (T³ and/or T², T) wasprone to variation over time, this variation being conveyed essentiallyas a drift in the frequency for a given temperature, the shape of thecurve f(T³ and/or T², T) remaining substantially unchanged.

To obtain a method of calculating the acceleration γ which remainsaccurate over time, it is very desirable to provide for a recalibrationas illustrated in FIG. 4 of the appended drawings.

With this aim, the steps described previously are supplemented with thefollowing steps appearing in FIG. 4 (which is derived more preciselyfrom FIG. 3A). The derivative with respect to time dT_(mes)/dt iscalculated at 22 on the basis of the measured value of the temperatureT_(mes). If, at 23, this drift is detected to be zero or almost zero,then a recalibration procedure RECAL is instigated at 24, able to act onthe transfer function held in memory at 16, on the calculation/selectionat 13 of the possible values of temperature T_(a), T_(b), and on thecalculation 21 of the value f₁−f₂=p+q γ+r T leading, in a simple way, tothe determination of the acceleration γ.

Finally, it will be noted that the acceleration γ is calculatediteratively, by successive calculation passes, and that each calculationpass takes into account the value of the acceleration found at theconclusion of the previous calculation pass, in particular for thecompensation of the sum f₁+f₂ mentioned above when k₁≠k₂.

In practice, several vibrating devices may be grouped together toprovide accelerometric and/or gyrometric or gyroscopic information intwo or three reference axes (for example inertial sensor block), allthese vibrating devices calling individually upon a temperaturemeasurement for the determination of the compensated values of thevibration frequencies.

According to the invention, the temperature-compensated accelerometricand/or gyroscopic and/or gyrometric measurement, performed for eachdevice having two vibrating resonators, takes into account not only itsown weighted temperature value, but also at least certain weightedtemperatures predetermined for other vibrating devices so as to obtainan interpolated frequency value related to at least a certain number ofthe measured temperatures.

By way of example, represented very schematically in FIG. 5 is aninertial sensor 28 grouping together three vibrating devices foraccelerometric measurements in three axes x, y, z of a reference frame,each vibrating device possibly being of the type illustrated in FIG. 2and being referenced 1 ¹ _(x), 1 ¹ _(y)and 1 ¹ _(z) respectively, aswell as three vibrating devices for gyroscopic measurements with respectto the three axes x, y, z of the reference frame, each vibrating devicepossibly being of the type illustrated in FIG. 2 and being referenced 1² _(x), 1 ² _(y)and 1 ² _(z) respectively.

With each aforesaid vibrating device is associated an informationprocessing unit that receives the information f₁, f₂ and T_(mes)provided by each device. As illustrated in FIG. 6, each unit 27 isarranged (by way of example) in accordance with the representation givenin FIG. 3A. FIG. 6 shows, by way of example, the unit 27 ¹ _(x)associated with the vibrating device 1 ¹ _(x), it being understood thatthe other units associated respectively with the other vibrating devicesare identical to it.

All the weighted temperature values determined by all the units 27, T¹_(x), T¹ _(y), T¹ _(z), T² _(x), T² _(y), T² _(z) are sent to acorrelation device 29 which, on the basis of a pre- establishedcorrelation (for example calculation of the mean), delivers a correlatedvalue of temperature T_(c), which is thereafter delivered to each unit27.

In the unit 27, the correlated value T_(c) may then be used directly at21 to calculate, from f₁−f₂, the value of the component of acceleration(γ¹ _(x) in FIG. 6).

It is also conceivable, as illustrated in FIG. 7 which shows only a partof the unit 27 ¹ _(x) for the correlated value of temperature T_(c) tobe combined, according to a pre-established law, at 30, with theweighted value T¹ _(x) the resulting value being used for thecalculation of the component γ¹ _(x) from the value f₁−f₂.

Of course, numerous variants of temperature correlation are conceivable,for example: correlation in respect of the temperatures of theaccelerometric vibrating devices alone and correlation in respect of thetemperatures of the gyroscopic vibrating devices alone;cross-correlation between the temperatures of the accelerometric andgyroscopic devices; etc.

An economic advantage may be obtained when all the vibrating devices aremachined from one single block of crystal or “wafer”. The vibratingdevices are then situated in immediate proximity to one another andthere is no longer any need to assign a temperature sensor to each ofthem: according to the configuration of mutual layout of the devices, asingle temperature sensor disposed centrally may suffice, or at the veryleast two temperature sensors may be envisaged, one associated with thevibrating devices for accelerometric measurements and the other with thevibrating devices for gyroscopic or gyrometric measurements. A gain indimension in respect of the substrate and a saving as regards theinformation processing capacity is thus achieved.

It is in particular in the case of the implementation of severaladjacently located vibrating devices that it may be appropriate toprocess a magnitude G representative of the temperature without callingupon the temperature itself. Such a case may arise for example when thedevice 1 having two vibrating resonators of frequency f₁ and f₂ issupplemented with an adjacently adjoining vibrating device such as agyroscopic resonator of the so-called “bowl” type, whose resonantfrequency varies linearly as a function of temperature and may bewritten f=mt+n where m and n are constants. It is then understood thatmeasuring the frequency f of this vibrating device provides atemperature indication which, to within a constant, is equivalent to adirect measurement of the temperature with the aid of a temperaturesensor.

Hence, the processing of aforesaid magnitude G(T), if the latter variesin a simple manner as a function of temperature, makes it possible toproceed with the method of accelerometric measurement according to theinvention without it being necessary to implement an actual temperaturesensor.

It is an arrangement of this type that is illustrated in FIG. 8, thediagram of which mimics that of FIG. 3A. At 15 is measured the valueG_(mes) of a magnitude G(T) in particular in a vibrating device adjacentto the device 1 having two vibrating resonators of frequency f₁ and f₂,said magnitude G(T) thus being representative of the temperature inproximity to said vibrating device 1. Then, with the aid of a transferfunction H previously established at 16, an estimated valueG_(estimated)=H(G_(mes)) of the abovementioned magnitude G(T) isdetermined, the estimated value G_(estimated) being representative ofthe estimated temperature of the vibrating resonators of frequency f₁and f₂. It is this value G_(estimated) that is used thereafter, inconjunction with the values T_(a), T_(b), to determine the probabilitiesP(T_(a)) and P(T_(b)) mentioned above, without in fact involving thevalue of the estimated temperature T_(estimated).

Such a solution has the benefit of avoiding the implementation of one ormore temperature sensors, this being advantageous from the economicstandpoint. Furthermore, the eliminating of one or more hardwarecomponents in an inertial sensor block is always particularly welcome byreason of the gain of space and of bulk thus obtained which goes hand inhand with the search for ever more compact inertial sensor blocks.

1. A method for accelerometer measurement by determination of the value,compensated as a function of temperature, of an acceleration on thebasis of determinations of frequencies made on at least oneaccelerometer device having two vibrating resonators of similargeometries working respectively in stress states of opposite signs,characterized in that it comprises the steps which follow: the devicebeing subjected to a component of acceleration (γ), the frequencies f₁(at 10) and f₂ (at 11) of the respective vibrations of the two vibratingresonators are determined, given that the respective values of these twofrequencies are influenced by the acceleration (γ) and by thetemperature (T); the sum f₁+f₂ of the two determined frequencies isdetermined (at 12), given that this sum is influenced by thetemperature; on the basis of a pre-established correlation of thevariation of the quantity f₁+f₂ as a function of temperature (at 14),the possible temperature values T_(i) corresponding to the value of theabove determined sum f₁+f₂ are plotted (at 13); the value (G_(mes)) of amagnitude representative of the temperature in proximity to the devicehaving two vibrating resonators is measured; with the aid of apreviously established transfer function H, an estimated valueG_(estimated)=H(G_(mes)) of above said magnitude is determined on thebasis of said measured value (G_(mes)), this estimated magnitude beingrepresentative of the estimated temperature of the vibrating resonators;on the basis of the estimated value (G_(estimated)) of said magnitudeand of the possible temperature values (T_(i)), the probabilitiesP(T_(i)) that each possible value (T_(i)) is the exact value of thetemperature of the resonators is determined (at 18), for each possiblevalue (T_(i)); a weighted value T of the temperature of the vibratingresonators is calculated (at 19) T=ΣP(T_(i))×T_(i); and on the basis ofone or more determined frequencies f₁ and f₂ and of the weighted value Tof the temperature, the temperature-compensated value of theacceleration undergone by the accelerometer device is determined (at21).
 2. The method as claimed in claim 1, characterized in that the sumof the frequencies (f₁+f₂)is corrected, so as to take account ofgeometrical differences between the two vibrating resonators, with anerror term estimated on the basis of the acceleration calculated duringthe previous calculation cycle, if it exists.
 3. The method as claimedin claim 1, characterized in that the influence of the temperature onthe value of the vibration of each vibrating resonator is conveyed by apolynomial of order 2: Σ(T²) or by a polynomial of order 3: Σ(T³), andin that, in above said series of steps of the method, the two possibletemperature values (T_(a), T_(b)) corresponding to the value of theabove determined sum of the frequencies (f₁+f₂)are plotted (at 13) onthe basis of the pre-established (at 14, 25, 26) correlation of thevariation of the sum of the measured frequencies (f₁+f₂)as a function oftemperature; and the probability (P(T_(a))) that the temperature of theresonators is one of these temperatures (T_(a)) and the probability(P(T_(b))) that the temperature of the resonators is the other of thesetemperatures (T_(b)) are determined (at 18) on the basis of theestimated value (G_(estimated)) of said magnitude (at 17) and of the twopossible temperature values (T_(a), T_(b)), then a weighted value of thetemperature is calculated (at 19)T=P(T_(a))·T _(a) +P(T_(b))·T_(b).
 4. The method as claimed in claim 3,characterized in that the pre-established correlation is a mathematicalfunction of second or third degree, held in memory (at 14), representingthe variation of the frequencies as a function of the temperatureestablished for the relevant accelerometer device having two vibratingresonators.
 5. The method as claimed in claim 3, characterized in thatthe pre-established correlation is a correspondence table held in memory(at 14), giving, for each value of the frequency (f₁+f₂), the twopossible values (T_(a), T_(b)) of the temperature.
 6. The method asclaimed in claim 1, characterized in that the transfer function (H) is amathematical function held in memory (at 16) and establishedexperimentally for the relevant accelerometer device having twovibrating beams.
 7. The method as claimed in claim 1, characterized inthat the transfer function (H) is a table held in memory (at 16) andgiving a pre-established correspondence between each measured value(G_(mes)) and an estimated value (G_(estimated)).
 8. The method asclaimed in claim 1, characterized in that a readjustment is performed(at 22 to 24) on the transfer function (H), on the selection of thepossible temperature values (T_(i)) and on the final calculation when adrift is noted in the curve of the correlation between frequency andtemperature.
 9. The method as claimed in claim 1, characterized in thatthe frequencies (f₁, f₂) of the respective vibrations of the twovibrating resonators are measured.
 10. A method of accelerometric and/orgyroscopic and/or gyrometric measurements in several axes with the aidof several respective accelerometric and/or gyroscopic and/or gyrometricvibrating devices, characterized in that, in each axis, a value of thetemperature-compensated acceleration is determined according to claim 1,and in that, for the determination of one at least of the values of thetemperature-compensated acceleration, the weighted value of temperaturedetermined for the vibrating device associated with this axis togetherwith at least one weighted value of temperature determined for at leastone vibrating device associated with at least one other axis are used asweighted temperature value.
 11. The method of accelerometric and/orgyroscopic and/or gyrometric measurement in several axes as claimed inclaim 10, characterized in that all the vibrating resonators of theaccelerometric and/or gyroscopic and/or gyrometric devices are machinedfrom one and the same block of crystal.
 12. The method as claimed inclaim 1, characterized in that the magnitude representative of thetemperature in proximity to the device having two vibrating resonatorsis the temperature (T_(mes)) itself which is measured (at 15) inproximity to the device having two vibrating resonators, and in thatwith the aid of the transfer function H previously established (at 16),an estimated value T_(estimated)=H(T_(mes)) of the temperature of thevibrating resonators is determined (at 17) on the basis of the measuredvalue (T_(mes)).
 13. The method as claimed in claim 12, characterized inthat the temperature (T_(mes)) is measured outside a box of the devicethat encloses the two vibrating resonators.
 14. The method as claimed inclaim 12, characterized in that the temperature (T_(mes)) is measuredinside a box of the device that encloses the two vibrating resonators.15. The method as claimed in claim 10, characterized in that one atleast of the vibrating devices has a resonant frequency that varieslinearly as a function of temperature and in that it is this linearlytemperature dependent frequency that is measured and used as magnituderepresentative of the temperature.